A browser-based notebook for review and re-use of previous inputs and outputs, including graphics and text annotations. Compatible with Firefox, Opera, Konqueror, Google Chrome and Safari. Notebooks can be accessed locally or remotely and the connection can be secured with HTTPS.

Rather than reinventing the wheel, Sage (which is written mostly in Python and Cython) integrates many specialized mathematics software packages into a common interface, for which a user needs to know only Python. However, Sage contains hundreds of thousands of unique lines of code adding new functions and creating the interface between its components.[11]

SageMath uses both students and professionals for development. The development of SageMath is supported by both volunteer work and grants.[12] However, it was not until 2016 that the first full-time Sage developer was hired (funded by an EU grant).[13] The same year, Stein described his disappointment with a lack of academic funding and credentials for software development, citing it as the reason for his decision to leave his tenured academic position to work full-time on the project in a newly founded company, SageMath, Inc.[13]

Only the major releases are listed below. SageMath practices the "release early, release often" concept, with releases every few weeks or months. In total, there have been over 300 releases, although their frequency has decreased.[14]

SageMath versions

Version

Release Date

Description

0.1

January 2005

Included PARI, but not GAP or Singular

0.2–0.4

March to July 2005

Cremona's database, multivariate polynomials, large finite fields and more documentation

Both binaries and source code are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as ATLAS, FLINT, and NTL will be tuned and optimized for that computer, taking into account the number of processors, the size of their caches, whether there is hardware support for SSE instructions, etc.

Cython can increase the speed of SageMath programs, as the Python code is converted into C.[22]

The source code can be downloaded from the downloads page. Although not recommended for end users, development releases of SageMath are also available. Many Linux distributions also include SageMath in their repositories [see below].

Binaries can be downloaded for Linux, macOS and Solaris (both x86 and SPARC).

A live CD containing a bootable Linux operating system is also available. This allows usage of SageMath without Linux installation.

Users can use an online "single cell" version of SageMath at sagecell.sagemath.org or embed a single SageMath cell into any web page. Users can also create permalinks to SageMath computations using the cell server.[23]

Although Microsoft was sponsoring a native version of SageMath for the Windows operating system, prior to 2016 there were no plans for a native port, and users of Windows had to use virtualization technology such as VirtualBox to run SageMath.[24] As of SageMath 8.0 (July 2017), with development funded by the OpenDreamKit project[13], it successfully builds on Cygwin, and a binary installer for 64-bit versions of Windows is available.[25]

Linux distributions in which SageMath is available as a package are Mandriva, Fedora, Arch Linux, Debian and NixOS. It is also available as a dedicated UbuntuPPA.[26] In Gentoo, it's available via layman in the "sage-on-gentoo"[27] overlay. However, SageMath can be installed to any Linux distribution.

A=matrix([[1,2,3],[3,2,1],[1,1,1]])y=vector([0,-4,-1])A.solve_right(y)# returns (-2, 1, 0)A.eigenvalues()# returns [5, 0, -1]B=matrix([[1,2,3],[3,2,1],[1,2,1]])B.inverse()# returns[01/2-1/2][-1/4-1/41][1/20-1/2]# same matrix, but over the ring of doubles (not rationals, as above)sage:B=matrix(RDF,[[1,2,3],[3,2,1],[1,2,1]])sage:B.inverse()[-5.55111512313e-170.5-0.5][-0.25-0.251.0][0.50.0-0.5]# Call NumPy for the Moore-Penrose pseudo-inverse, # since SageMath does not support that yet.importnumpyC=matrix([[1,1],[2,2]])matrix(numpy.linalg.pinv(C))# returns[0.10.2][0.10.2]

prime_pi(1000000)# returns 78498, the number of primes less than one millionE=EllipticCurve('389a')# construct an elliptic curve from its Cremona labelP,Q=E.gens()7*P+Q# returns (24187731458439253/244328192262001 : # 3778434777075334029261244/3819094217575529893001 : 1)